If you bought the game and you don't have your season pass and nuketown, try verifying your game cache by right clicking on the game in the list part of the Library (where it lists all of your games to the left) and pressing properties. From there, go to the Local Files tab and it should be the bottom button.
You can also check if you have the Season Pass and Nuk3Town map DLC downloaded by going to the DLC tab in the game's properties and looking for Black Ops III - Season Pass and Black Ops III - NUK3TOWN Bonus Map. If there is no check mark by the side of those two (if they are listed), click on the two check boxes and wait for them to install. It shouldn't take that long.